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Analysis of Nonlinearity Correction
for CrIS SDR
April 25, 2012
Chunming Wang NGAS
Comparisons Between V32 and V33 Engineering Packets
2
Expected Linearity Improvement Using v33 Engineering Packet Parameters is Confirmed
• Detailed analyses of residual nonlinearity were performed using the Golden Days data and data from April 15, 2012
– Convergence of statistics were examined
– Distribution of scene brightness temperature, FOV to FOV differences in brightness temperatures were examined
• Stratification of statistics using mean brightness temperature for each FOR provided valuable information on linearity of the detectors
– Change in the magnitude of nonlinearity as a function of mean brightness temperature relative to ICT were analyzed
– Sensitivity of brightness temperature to small radiance variation for low temperature scene were taken into consideration
• Expected improvement in linearity using v33 parameters is confirmed– Independent processing of RDR using NGAS off-line code provided additional
confirmation
Updated Parameters Substantially Improves Linearity of CrIS SDR
3
IDPS Generated SDR Products for April 15 Were Used in the Analyses
February 24 April 15
• Standard IDPS SDR products showed stable quality– No obvious anomalous radiances were detected; small data gap is due to delay in
data delivery to NGAS
– Expected warming in Northern hemisphere and cooling in Southern hemisphere were visible
4
Differences in Brightness Temperatures of LWIR FOVs from FOR Mean Were Reduced
February 24 April 15
• Ensemble averages of brightness temperature difference of each FOV to the FOR mean were substantially reduced
– All Earth scenes were used without rejection by variation in brightness temperatures among 9 FOVs
– Standard deviations of the differences due to geometric effects were unchanged
FOV5 FOV5
Side FOVs Side FOVs
Corner FOVs Corner FOVs
5
Meam Differences in Brightness Temperatures Among MWIR FOVs Were Greatly Reduced
• Substantial improvement for FOV7 and FOV8 were observed– FOV7 and FOV8 are now in family with the rest of FOVs
– Residual differences are at similar magnitude as the difference between FOV9 and FOV6 which were shown to be basically linear during TVAC tests
February 24 April 15
6
Statistics of SWIR FOVs Were Unchanged Due to Identical Processing Parameters
February 24 April 15
• The brightness differences from FOV to FOV were substantial– In-depth analysis of the distribution of these differences show the detectors are
basically linear
– Brightness temperature differences seem to be linked to geometry
Analyses Methodology
8
Key Issues Concerning the Analysis Methodology Were Investigated
• Convergence of statistics is achieved using one day of data – One or two orbits data may not be sufficient
– Convergence in average brightness temperature is slower than average differences from FOR mean
• Effect of scene brightness relative to ICT is taken into consideration– When scene brightness if very close to that of ICT nonlinearity effect is minimized
– At very low temperature scene brightness temperature is sensitive to radiance uncertainty
• Separation of nonlinearity from other sources of errors– Identify signatures of nonlinearity
– Independent processing of RDR using NGAS off-line code provided additional confirmation
Confidence in Conclusion is Gained by the Validation of Methodology
9
Using Spectrally Averaged Channel Brightness Temperature Reduces Effects of ILS Errors
• Spectral resampling helps reduce effects of spectral calibration uncertainties
– Averaging in brightness temperatures space is preferred because of the flatness of Earth scene spectra in brightness temperature
• Nonlinearity is an effect on the broad spectrum
– Overall nonlinearity is a function of the radiance energy over the entire band
– Spectral resampling does not affect dynamic range of spectra
10
Convergence of Brightness Difference Requires Averaging Over 3 Orbits of Data
• Convergence of mean brightness temperature is slow due to bi-modal distribution of radiances
– Mean brightness temperatures for all FOV changes simultaneously
– It requires more than 3 orbits of data to bring the average FOV to FOV difference to within 10% of its final value
Co
nve
rge
nce
of
Sp
ect
raC
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verg
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Diff
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R m
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Co
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of
Dis
trib
utio
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f E
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h S
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e B
righ
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ss
11
Convergence of Brightness Difference Requires Averaging Over 3 Orbits of Data
• Convergence for MWIR seems faster than LWIR band
– More than 2 orbits of data is required to bring the average FOV 2 FOV differences in brightness temperature to within 10% of its final value
Co
nve
rge
nce
of
Sp
ect
raC
on
verg
en
ce o
f D
istr
ibu
tion
of
Diff
ere
nce
to
FO
R m
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n
Co
nve
rge
nce
of
Dis
trib
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f E
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h S
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e B
righ
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12
Brightness Temperature Error Due to Nonlinearity Depends on Scene Brightness
BT Range, smoothed channels
BT RangeDesignatedWindow channels
ICT TemperatureMin,Max
Mean BT
• Earth scene spectrum has different brightness temperature for all channels
• Warmest channels carry most of photon energy
– A subset of window channels is selected for each band to represent the brightness of the scenes
– Average of all FOVs is used to classify the brightness of a scene
13
Each Earth Scene (FOR) is Classified into one of 50 Groups According to Its Brightness
• Bi-modal distribution of the Earth scene brightness is consistent with channel brightness statistics
– Large number of Earth scenes are warmer than ICT
– Since Earth scene spectrum is not constant in brightness the total energy is lower than black body at the same brightness
• ICT temperature varies over a very small range
14
FOV-to-FOV Brightness Temperature Differences Depend on Scene Temperature
High Temperature Scenes Low Temperature Scenes
LWIR
MWIR
SWIR
FOV6-FOV9
FOV6-FOV9
15
Examination of the Joint Probability Distribution Reveals Scene Dependence of BT Differences
February 24LWIR932.5 cm-1
Sce
ne
Brig
htn
ess
BT DifferenceFrom FORMean
16
Wider Spread of Distributions in BT Difference for Cooler Scene is Due to Higher Sensitivity
• Constant perturbation in radiance space leads to larger changes in brightness temperature for cooler scenes
– Wider spread of difference in brightness temperature among FOVs is due in part of this sensitivity
• Very warm scenes are also more likely to be cloud free
– Cloud free scene may be more uniform than cloudy scenes
17
Examination of Joint Probability Distribution for MWIR FOV Helps Us Recognize Nonlinearity
Nonlinear FOV
Linear FOV
February 24,2012MWIR1275 cm-1
Large Difference Away
from Calibration Points
18
Correction with v33 Engineering Parameters Nearly Completely Removed Nonlinearity
April, 152012MWIR1275 cm-1
19
Residual Nonlinearity for LWIR Are Significantly Reduced for FOV9 with v33 Parameters
April 15LWIR932.5 cm-1
20
Examination of the Joint Probability Distribution Shows SWIR Detectors Are Mostly Linear
February 24SWIR2535 cm-1
21
Statistical Results for SWIR Band Are Highly Consistent for Two Focus Days
April 15SWIR2535 cm-1
22
Empirical Data from Two Days Seem to Suggest Geometric Trend in BT Bias for SWIR
• Brightness temperature biases seem to be linked to the position of the FOVs
– Both days of data show the similar trend
• More in-depth analyses are needed to determine the cause of these biases
– Analyses of DS and ICT raw spectra are needed
FOV2FOV1 FOV3
FOV5FOV4 FOV6
FOV8FOV7 FOV9
23
Conclusion
• Residual nonlinearity for all detectors are very small– Joint probability distribution of the Earth scene brightness and brightness
difference is very useful in identifying nonlinearity
– SWIR detectors are all linear
• SWIR band FOV-to-FOV biases may be caused by non-uniformity of the calibration targets
– More analyses are on-going
• Methodology can be used to monitor nonlinearity